$A$ cell of emf $E$ is connected to a resistance $R_{1}$ for time $t$ and the amount of heat generated in it is $H$. If the resistance $R_{1}$ is replaced by another resistance $R_{2}$ and is connected to the cell for the same time $t$,the amount of heat generated in $R_{2}$ is $4H$. Then the internal resistance $r$ of the cell is:

In a thermocouple,the temperature that does not depend on the temperature of the cold junction is called

Two $220\; V, 100\; W$ bulbs are connected first in series and then in parallel. Each time the combination is connected to a $220\; V\; AC$ supply line. The power drawn by the combination in each case respectively will be

When an electric heater is switched on, the current flowing through it $(I)$ is plotted against time $(t)$. Taking into account the variation of resistance with temperature, which of the following best represents the resulting curve?

The production of $e.m.f.$ by maintaining a difference of temperature between the two junctions of two different metals is known as

Shown in the figure is a semicircular metallic strip that has thickness $t$ and resistivity $\rho$. Its inner radius is $R_1$ and outer radius is $R_2$. If a voltage $V_0$ is applied between its two ends,a current $I$ flows in it. In addition,it is observed that a transverse voltage $\Delta V$ develops between its inner and outer surfaces due to purely kinetic effects of moving electrons (ignore any role of the magnetic field due to the current). Then (figure is schematic and not drawn to scale)-
$(A)$ $I = \frac{V_0 t}{\pi \rho} \ln \left(\frac{R_2}{R_1}\right)$
$(B)$ the outer surface is at a higher voltage than the inner surface
$(C)$ the outer surface is at a lower voltage than the inner surface
$(D)$ $\Delta V \propto I^2$